• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

zpbtrs - solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF

SYNOPSIS

  SUBROUTINE ZPBTRS( UPLO, N, NDIAG, NRHS, A, LDA, B, LDB, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX A(LDA,*), B(LDB,*)
  INTEGER N, NDIAG, NRHS, LDA, LDB, INFO

  SUBROUTINE ZPBTRS_64( UPLO, N, NDIAG, NRHS, A, LDA, B, LDB, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX A(LDA,*), B(LDB,*)
  INTEGER*8 N, NDIAG, NRHS, LDA, LDB, INFO

F95 INTERFACE

  SUBROUTINE PBTRS( UPLO, [N], NDIAG, [NRHS], A, [LDA], B, [LDB], 
 *       [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8), DIMENSION(:,:) :: A, B
  INTEGER :: N, NDIAG, NRHS, LDA, LDB, INFO

  SUBROUTINE PBTRS_64( UPLO, [N], NDIAG, [NRHS], A, [LDA], B, [LDB], 
 *       [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8), DIMENSION(:,:) :: A, B
  INTEGER(8) :: N, NDIAG, NRHS, LDA, LDB, INFO

C INTERFACE

#include <sunperf.h>

void zpbtrs(char uplo, int n, int ndiag, int nrhs, doublecomplex *a, int lda, doublecomplex *b, int ldb, int *info);

void zpbtrs_64(char uplo, long n, long ndiag, long nrhs, doublecomplex *a, long lda, doublecomplex *b, long ldb, long *info);

PURPOSE

zpbtrs solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF.

ARGUMENTS

• UPLO (input)
  

   = 'U':  Upper triangular factor stored in A;

   = 'L':  Lower triangular factor stored in A.

• N (input)
  The order of the matrix A. N > = 0.

• NDIAG (input)
  The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. NDIAG > = 0.

• NRHS (input)
  The number of right hand sides, i.e., the number of columns of the matrix B. NRHS > = 0.

• A (input)
  The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H of the band matrix A, stored in the first NDIAG+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array A as follows: if UPLO ='U', A(kd+1+i-j,j) = U(i,j) for max(1,j-kd) < =i < =j; if UPLO ='L', A(1+i-j,j) = L(i,j) for j < =i < =min(n,j+kd).

• LDA (input)
  The leading dimension of the array A. LDA > = NDIAG+1.

• B (input/output)
  On entry, the right hand side matrix B. On exit, the solution matrix X.

• LDB (input)
  The leading dimension of the array B. LDB > = max(1,N).

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value